New Learning Composite Mathematics Class 5 S.K. Gupta Anubhuti Gangal Volume Chapter 18A Solution
New Learning Composite Mathematics Class 5 S.K. Gupta Anubhuti Gangal Volume Chapter 18A Solution by expert Math Teacher.
Self Practice 18A
New Learning Composite Class 5 Volume
1) The solids shown below are made of 1 cubes. Write the value of each of the following.
a)
Ans: The value of one cube is 1 cu cm. Number of cubes in the solid are = 10
The volume of the solid is 10 cu cm.
b)
Ans: The value of one cube is 1 cu cm. Number of cubes in the solid are = 16
The volume of the solid is 16 cu cm.
c)
Ans: The value of one cube is 1 cu cm. Number of cubes in the solid are = 125
The volume of the solid is 125 cu cm.
2) Find the volume of each solid and write the unit with your answer.
a)
Ans: The volume of cuboid = height × length × breadth
The volume = 12×14×8 cu cm [height = 12 cm, length = 14 cm, breadth = 8 cm]
= 1344 cu cm
b)
Ans: The volume of cuboid = height × length × breadth
The volume = 3×4.8×4 cu cm [height = 3 cm, length = 4.8 cm, breadth = 4 cm]
= 57.6 cu cm
c)
Ans: As we can see from the image given the height, length and breadth are equal to each other.
So the given shape is a cube.
Volume of a cube = (length of the edge)3 = 1.23 cu cm= 1.728 cu cm
3) For a cuboid, copy and complete the table:
Length |
Breadth | Height | Volume |
6 cm | 2 cm | 3 cm |
ANS – 36 cu cm |
0.8 cm |
2 cm | 4 cm | ANS – 6.4 cu cm |
8 mm | 4 mm | 6mm |
ANS – 192 cu mm |
1.2 cm |
0.8 cm | 6 cm | ANS – 5.76 cu cm |
5 m | 250 cm | 2.2 m |
ANS – 2.75 cu m |
1 4) Find the volume of the following cubes.
a) Edge 5 cm
Ans: Volume of the cubes = 53 cu cm = 125 cu cm
b) Edge 8 cm
Ans: Volume of the cubes = 83 cu cm = 512 cu cm
c) Edge 2.7 cm
Ans: Volume of the cubes = 2.73 cu cm = 19.683 cu cm
d) Edge 60 mm
Ans: Volume of the cubes = 603 cu mm = 216000 cu mm
e) Edge 10 mm
Ans: Volume of the cubes = 103 cu mm = 1000 cu mm
f) Edge 4.3 m
Ans: Volume of the cubes = 4.33 cu m = 79.507 cu m
5) A cube of edge 100 cm has the same volume as a cube of edge 1 m. How many cubic centimeters make 1 cubic metre?
Ans: In 1 cubic meter there are 100 cubic centimeters.
6) Bricks have been piled near a construction site. Pile is 5 dm wide, 9 dm long and 3 dm high. What is the volume of the pile of bricks?
Ans : The pile of brick is 5 dm wide, 9 dm long and 3 dm high
The volume of the brick pile is = 5×9×3 cu dm = 135 cu dm
7) Which has the greatest volume: box that measures 18 cm by 3 cm by 2 cm or one that measures 6 cm by 6 cm by 7 cm?
Ans:
Volume of the first box = 18×3×2 cu cm = 108 cu cm
Volume of the second box = 6×6×7 cu cm = 252 cu cm
The second box has greater volume than the first box.
8) Find the volume of the rectangular solids, whose dimensions are as follows.
a) Length 15 m, breadth 12 m, thickness 80 cm.
b) Length 10(1/2) m, breadth 4.2 m, thickness 70 cm.
Ans:
a) Volume of cuboids = length ×breadth ×height = 15 × 12 × 0.8 cu m = 144 cu m
b) Volume of cuboids = length ×breadth ×height = 10.5 × 4.2 × 0.7 cu m = 30.87 cu m
9) Calculate the volume of air in a six- room house. If the height of each room is 3 m and the lengths and widths of the room, in meters, are given in the following table.
Room |
A | B | C | D | E | F |
Length | 10 | 4 | 6 | 6 | 8 |
4 |
Width |
6 | 4 | 5 | 4 | 4 |
3 |
Ans:
A) Volume of room A = 10 ×6 ×3 cu m = 180 cu m
B) volume of room B = 4 × 4× 3 cu m = 48 cu m
C) Volume of room C = 6 × 5 × 3 cu m = 90 cu m
D) Volume of room D = 6 × 4 × 3 cu m = 72 cu m
E) Volume of room E = 8 × 4 × 3 cu m = 96 cu m
F) Volume of room F = 4 × 3 × 3 cu m = 36 cu m
10) Which of these cuboids could be build using 80 one-centimeter cubes?
a) 6 cm long, 5 cm wide, 4 cm high
The volume of this cuboid is = 6×5×4 cu cm = 120 cu cm
So this cuboid cannot be built by 80 one-centimeter cubes.
b) 8 cm long, 5 cm wide, 2 cm high
The volume of this cuboid is = 8×5×2 cu cm = 80 cu cm
So this cuboid can be built by 80 one-centimeter cubes
c) 10 cm long, 4 cm wide, 5 cm high
The volume of this cuboid is = 10×4×5 cu cm = 200 cu cm
So this cuboid cannot be built by 80 one-centimeter cubes.
d) 6 cm long, 7 cm wide, 2 cm high
The volume of this cuboid is = 6×7×2 cu cm = 84 cu cm
So this cuboid cannot be built by 80 one-centimeter cubes.
e) 7 cm long, 5 cm wide, 2 cm high
The volume of this cuboid is = 7×5×2 cu cm = 70 cu cm
So this cuboid cannot be built by 80 one-centimeter cubes.
f) 10 cm long, 4 cm wide, 2 cm high
The volume of this cuboid is = 10×4×2 cu cm = 80 cu cm
So this cuboid can be built by 80 one-centimeter cubes.
11) Write the length, breadth and height of six cuboids that can be made from 36 one-centimeter cubes
[Hint: find all factors of 36 and then various possible combinations of these factors so that the product remains 36]
Ans: The total volume of a cube made by 36 one-centimeter cube is 36 cu cm.
The factors of 36 are 1, 2, 2, 3 and 3
The 6 of the possible combinations of length, breadth and height for a cuboid of 36 cu cm are (1, 1, 36), (1, 2, 18), (1, 3, 12), (2, 2, 9), (2, 3, 6), (3, 3, 4).
12) A cuboid is 7 cm long, 4 cm wide and 3 cm high and a cube has an edge of 8 cm. which one has greater volume and by how much?
Ans: The volume of the cuboid of 7 cm length, 4 cm width and 3 cm height is = 7× 4× 3 cu cm. = 84 cu cm.
The volume of the cube with an edge of 8 cm = 83=216 cu cm.
The cube has a greater volume than the cuboid by 132 cu cm.
13) Volume of a cuboid is (1/4) cu m. What is its volume in cu cm?
Ans: The volume of the cuboid according to the question is (1/4) cu m = 0.25 cu m
If we want to convert cu m to cu cm than we have to multiply it by 1003.
∴ 0.25 cu m = 0.25×1003 cu cm=250000 cu cm
14) One centimeter, one square centimeter and one cubic centimeter are different measurements. Why?
Ans: One centimeter is a measure of length.
One square centimeter is a measure of area.
And one cubic centimeter is a measure of volume.
15) An underground tank was 30 m long and 2 m wide and 2 m deep. How many cubic meters of earth was removed to dig the tank?
Ans: The volume of the underground tank is 30×2×2 cu m = 120 cu m
So to make the underground tank 120 cu m earth was removed.
16) Complete the following table.
Length |
Breadth | Height | Volume |
4 cm | 2 cm | ? = 3 cm |
24 cm3 |
5 cm |
? = 3 cm | 3 cm | 45 cm3 |
? = 10.5 mm | 50 mm | 0.4 cm = 4 mm |
2100mm3 |
8 cm |
? = 0.6 cm | 0.5 cm |
2.4 cm3 |
[Hint: To find the unknown dimensions, divide the volume by the product of the given dimensions.]
17) Find the volume of a rectangular tank of base area 40 cm2 and height 6 cm.
Ans: The Volume of the rectangular tank = 40 × 6 cu cm = 240 cu m.
18) The volume of a cuboidal copper block is 270 cm3. If its length is 15 cm and its breadth is 6 cm, what is its height?
Ans: We know that, volume of a cuboid = height × length × breadth
∴ 270 = height ×15×6
Or, height = 3
The height of the copper cuboidal is 3 cm.
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